Why does sliding edge makes it slide being mirrored?
From my admittedly limited testing I believe it is a side effect of being in face selection mode.

By selecting the whole side face instead of only the desired edges you are unintentionally also edge-sliding the vertical edges perpendicular to the view plane. Somehow the tool's geometry calculation probably gets confused trying to slide both loops at the same time while sharing the same corner vertex.

You can see it behaves as expected when selecting two edges only, but behaves unexpectedly if the side face is selected instead.